Modular arithmetic

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

Where will the point stop after it has turned through 30 000 degrees? I took out my calculator and typed 30 000 ÷ 360. How did this help?

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

A country has decided to have just two different coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?

Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: ×2 and -5. What do you think?

Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?

Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?